[0001] This invention is directed to the method of hydraulically fracturing a subterranean
formation.
[0002] Hydraulic fracturing techniques have been extensively used for increasing the recovery
of hydrocarbons from subterranean formations. These techniques involve injecting a
fracturing fluid down a well into contact with the subterranean formation to be fractured.
Sufficiently high pressure is applied to the fracturing fluid to initiate and propagate
a fracture into the subterranean formation. It is generally considered that at depth
the fractures that are formed are vertical fractures. This is because at depth the
least principal stress in most formations is in the horizontal plane which produces
a preferred vertical fracture orientation. Propping agents are generally entrained
in the fracturing fluid and are deposited in the fracture to maintain the fracture
open.
[0003] Hydraulic fracturing is widely practiced to increase the production rate from oil
and gas wells. Fracturing treatments are usually performed soon after the formation
interval to be produced is completed, that is, soon after fluid communication between
the well and the reservoir interval is established for the purpose of production or
injection. Wells are sometimes fractured for the purpose of stimulating production
after significant depletion of the reservoir.
[0004] Hydraulic fracturing is the principal method used for stimulating production from
oil and gas wells in low permeability reservoirs. Almost all of such fractures are
vertical. It is always desirable, and sometimes necessary, to limit the vertical extent
(height) of such fractures to the hydrocarbon-bearing zone of interest while extending
the fracture for a substantial horizontal distance. Frequently, the desired horizontal
extent (length) is many times the desired height. The desired result can be readily
obtained when the interval to be fractured is bounded above and below by beds which
inhibit the growth of fractures, such as soft shades. In many other cases the bounding
beds are not effective in inhibiting the vertical growth of fractures. This is a major
limitation of application of hydraulic fracturing technology. In such cases the resulting
fracture grows into the non-productive bounding beds, and some of the valuable fracturing
materials are wasted. In cases where permeable beds containing unwanted fluids, such
as water, are also penetrated by the fracture a large amount of unwanted fluid is
introduced through the fracture into the producing well. In cases where the amount
of such unwanted fluid is prohibitive, the well has to be abandoned.
[0005] The present invention seeks to provide a method for controlling the vertical growth
of a hydraulic fracture in a subterranean formation located adjacent to another subterranean
formation in which the propagation of the fracture is to be inhibited.
[0006] Accordingly, the invention resides in a method of fracturing a subterranean formation
that is located adjacent another formation in which fracturing is to be inhibited,
comprising the steps of:
a. determining the fracturing gradient in the subterranean formation to be fractured,
b. determining the fracturing gradient in the adjacent formation wherein fracturing
is to be inhibited,
c. determining from said fracturing gradients the fracturing fluid density necessary
to inhibit the propagation of fracturing into said adjacent formation,
d. selecting a fracturing fluid with the necessary density for inhibiting the propagation
of said fracturing into said adjacent formation more than said specified vertical
distance, and
e. fracturing said subterranean formation with said fracturing fluid.
[0007] The accompanying drawing illustrates a wellhead penetrating a plurality of subsurface
formations, one of which is being fractured by a method according to one example of
the present invention.
[0008] Referring to the drawing a well 10 extends from the surface of the earth into subsurface
formations 11-15. The well 10 is equipped with casing 16 surrounded by cement 17 which
prevents communication in the well outside the casing between the subsurface formations.
Communication with a subsurface formation that is hydrocarbon bearing is established
by perforations, such as perforations 18, extending into subsurface formation 13 for
example. To enhance production from hydrocarbon bearing formation 13 a fracturing
treatment is performed through the perforations 18, thereby producing the vertically
disposed fracture 19.
[0009] It is a specific feature of the present method to inhibit the growth of fracture
19 and prevent it from penetrating through non-permeable formations, such as 12 and
14, into permeable formations which contain unwanted fluids, such as 11 and 15. Fracture
19 is shown as tending to grow upward into formation 12. Since fracture growth is
dominated by the magnitude of the least principal in-situ stress, the stress normal
to the fracture plane in formation 12 is not much greater than that in formation 13.
[0010] The least principal stress can be expressed as a fracturing gradient g
f, which is the least principal stress S
h divided by the depth Z, that is:
[0011] 
[0012] In order for the fracture to propagate, the fluid pressure in the fracture must exceed
S
h. The fluid pressure in the fracture increases linearly with depth, depending on the
fluid density, the total pressure at any point being P
0 + Pgh, where P is the pressure at a reference point Z
0 in the fluid, is the fluid density, g is gravitational acceleration, and h is the
vertical distance from the reference point Z
O, positive downward. Fluid pressure gradients due to vertical flow in the fracture
have been neglected. In practice, it is convenient to express the fluid pressure gradient
relative to the gradient g
w in pure water, which


[0013] The above information is now used to inhibit the tendency of fracture 19 to grow
upward. This is best seen from the following example. Suppose the fracturing gradients
g
f of formation 13 and g
f of formation 12 are determined to be 0.70 psilft (15.83 kPa/m). The fluid pressure
in the fracture becomes:

[0014] Letting the reference point Z
O be the bottom of formation 13, the fracture is propagated as follows:

[0015] Letting the fracturing fluid be water, then the pressure at any point in the fracture
P
Z is:

since h is positive downward the pressure P is less than P .
[0016] Thus, the pressure P
fz to fracture at any point Z above Z
0 is:

where [h] is the absolute value of h.
[0017] Thus, the fracture will have a strong tendency to propagate upward. In order to inhibit
this tendency, we must use a fracturing fluid with a density such that:
p > 0.70 (8.33 ppg)> 13.56 ppg (ppg = pounds per gallon). 0.43 > 1.63 kg/l
[0018] To provide a margin of safety, a fluid weighing 14 to 15 ppg (1.68 to 1.80 kg/1)
should be selected.
[0019] From the above example, we see that fractures tend to grow upward for formations
with equal fracture gradients which are in the normal range (0.60 to 0.90 psi/ft [13.57
to 20.36 kPa/m]). Fracture gradients usually, but not always, increase with depth.
[0020] A case of downward fracture growth and means for inhibiting, such growth will now
be described for an example in which the fracturing gradient in formation 13 is 0.70
psi/ft (15.83 kPa/m) and the gradient in formation 14 is 0.69 psi/ft (15.61 kPa/m).
The fracturing pressure at Z
O, the bottom of formation 13, is 0.70Z
o. The fracturing pressure in bed 14 at any point
Zo + h is:

[0021] Just below formation 13 the fracturing pressure in formation 14 is lower than in
formation 13 by 0.70 Z
o - 0.69 Z
o or 0.01 Z
o. Thus, the fracture will have a strong tendency to propagate into bed 14. In order
to propagate the fracture in formation 13 without continuing to propagate downward
in formation 14, P
Z must be:

This requires:


[0022] If we let Z
0 = 5000 ft. (1524 m), we need 0.69 h > 50 or h> 72.4 ft (22.1 m). But we must also
allow for the fracturing fluid head. This requires an additional h, = A h, to balance
the fluid head against the fracture gradient difference. This requires:


[0023] If the fracture penetrates 100 ft. (30.5 m) into formation 14, then:

and

[0024] The means available for adjusting p /P
o are selection of fracturing fluids with different density, selection of different
concentrations of propping agent, and selection of propping agents with different
density. Any practical combination of fluid, propping agent, and propping agent density
may be used.
[0025] The means for determining the fracturing gradient include direct measures of the
fracturing pressure and correlations such as these described by Breckels, I. M. and
Van Eekelen, H. A. M., "Relationship Between Horizontal Stress and Depth in Sedimentary
Basins," Journal of Petroleum Technology, September, 1982, pp. 2191-2199. Pny other
suitable means may be used.
[0026] The means of adjustment of fluid density will now be illustrated. In the forgoing
examole for an upward growing fracture a fluid with density greater than 13.56 ppg
(1.63 kg/1) is needed. This can be achieved by dissolving a suitable amount of sufficiently
soluble and dense salt in water, along with gelling agents, etc., for example, sodium
bromide. However, it will generally be more economical to achieve the desired density
by adding a suitable amount of propping agent to the aqueous fluid. Part of the increase
in density can be achieved, if desired, by dissolving inexpensive salts, such as sodium
or calcium chloride, in aqueous fluid. In non-aqueous fluids, the same type of procedure
can be followed.
[0027] The density of a fluid containing solids
pfs, such as propping agents, is given by:

where
Pf is the fluid density, C
f is the fraction of unit volume occupied by the fluid, p
s is the solid density and C
s is the fraction of unit volume occupied by solid. The density of fracturing fluids
and the concentration of solids contained therein is usually expressed in pounds per
gallon, ppg:

where V
s is the fraction of propping agent in the slurry. The volume of propping agent in
one gallon is:

where Psis the sand grain density in ppg = 8.33 (2.65) = 22.07 (5.83 kg/1). To obtain
a water slurry density of 13.56 ppg (1.63 kg/1) we need:



[0028] If a larger increase in density is required than is obtainable by sand, a sintered
bauxite or other agent may be used. If a still higher density is required, the density
of the base fluid may be increased by addition of a soluble salt.
[0029] To obtain a less dense fracturing fluid a low density liquid, such as diesel oil,
may be used. To obtain a still lower density, the aqueous or oil liquid may be mixed
with a gas to obtain a stable foam, as is well known to those skilled in the art of
hydraulic fracturing. The density of such foams, including propping agents if desired,
is calculated in a manner similar to that given above for an aqueous slurry.
[0030] From the forgoing examples, it is seen that control of the vertical growth of fractures
is exercised by control of the vertical pressure distribution within the fracturing
fluid. If inhibition of upward fracture growth is desired, a dense fracturing fluid
is used. If inhibition of downward fracture growth is desired, a light fracture fluid
is used. More particularly the fracturing gradients in the formation to be fractured
and in the adjacent formation where fracturing is to be inhibited are determined.
From this there is determined the fluid density necessary to negate the propagation
of the fracture into the formation where fracturing is to be avoided, or the fluid
density necessary to minimise penetration of the fracture into the formation to no
more than a specified vertical distance. A fracturing fluid is prepared which has
more than the minimum density desired if upward propagation is to be inhibited or
less than the maximum desired density if downward propagation is to be inhibited,
taking into account the amount of propping agent to be used in the fracturing fluid.
1. A method of fracturing a subterranean formation that is located adjacent another
formation in which fracturing is to be inhibited, comprising the steps of:
a. determining the fracturing gradient in the subterranean formation to be fractured,
b. determining the fracturing gradient in the adjacent formation wherein fracturing
is to be inhibited,
c. determining from said fracturing gradients the fracturing fluid density necessary
to inhibit the propagation of fracturing into said adjacent formation,
d. selecting a fracturing fluid with the necessary density for inhibiting the propagation
of said fracturing into said adjacent formation more than said specified vertical
distance, and
e. fracturing said subterranean formation with said fracturing fluid.
2. The method of Claim 1 wherein the density of said fracturing fluid is greater than
the minimum fracturing fluid density required for upward fracture growth.
3. The method of Claim 1 wherein the density of said fracturing fluid is less than
the maximum fracturing fluid density required for downward fracture growth.
4. The method of Claim 1 wherein to aid in the inhibition of upward fracture growth
the density of said fracturing fluid is increased by the addition of a granular solid
propping agent, sand, sintered bauxite, and/or a salt soluble in the fluid.
5. The method of Claim 1 wherein to aid in the inhibition of downward fracture growth
the density of said fracturing fluid is decreased by the addition of a low density
oil and/or a gas which forms a stable foam.
6. The method of Claim 1 wherein the fracturing fluid density is determined in accordance
with the following to inhibit upward fracture growth:
where: p = density of fracturing fluid in pounds per gallon,
po = density of water
gf = fracturing pressure gradient of formation being fractured,
gw = fluid pressure gradient in pure water
7. The method of claim 1 wherein the fracturing fluid density is determined in accordance
with the following to inhibit downward fracture growth:
where: p = density of fracturing fluid in pounds per gallon,
po = density of water (8.33 pounds per gallon),
gf = fracturing pressure gradient (psi/ft.) of formation being fractured,
gw = fluid pressure gradient in pure water